Lorenz gauge, derivative of field tensor

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SUMMARY

The discussion centers on the Lorenz gauge condition in electromagnetism, specifically the derivative of the field tensor, Fμν. The equation Fμν = ∂μAν - ∂νAμ is analyzed, leading to the expression ∂μFμν = ∂2μAν - ∂ν(∂μAμ). The term ∂ν(∂μAμ) drops out due to the equality of mixed partial derivatives and the assumption that ∂μAμ = 0 in the Lorenz gauge. This results in a simplification that is crucial for understanding gauge invariance in electromagnetic theory.

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Fμν = ∂μAν- ∂νAμ

μFμν = ∂2μAν - ∂ν(∂μAμ) = ∂2μAνWhy ∂ν(∂μAμ) and not ∂μνAμ ?

And why does ∂ν(∂μAμ) drop out?

thank you
 
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Because of the equality of mixed partial derivatives, [itex]\partial_\mu (\partial_\nu A_\mu) = \partial_\nu (\partial_\mu A_\mu)[/itex]. The Lorenz gauge assumes [itex]\partial_\mu A_\mu = 0[/itex], so that makes this term zero.
 
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